Chelsea face Milan in their third and final game in the International Champions Cup in the inaugural game in the spectacular new $1 billion US Bank stadium.
Conte will throw France midfielder Kante straight into action, so impressed has he been with the former Leicester star’s physical condition.
The Chelsea manager said: “Kante is in good shape. I found him in very good condition - now he is working on tactical aspects. But he is in good shape, he can certainly play one half or 30 minutes. He is ready.”
Conte on Saturday after Chelsea’s defeat against Real Madrid in Ann Arbor, in stark contrast, had said that he did not know if Costa, who has been chased all summer by his old club Atletico Madrid, would be staying.
Costa had missed the previous two games with a back problem, but Conte said: “Diego is Chelsea’s player, and that is the most important thing. He is very happy to stay with us.
Chelsea have tabled a renewed British record £65m bid for Everton striker Romelu Lukaku, and are also negotiating for £38m Napoli defender Kalidou Koulibaly.
Conte confirmed that there will be more transfer activity – in and out – before the season starts in two weeks time.
Tonight’s opponents Milan are chasing Chelsea’s Colombian winger Juan Cuadrado. The Serie A club want to secure a loan deal for a year for £8.5m - with a view to a permanent deal for a further £15m next summer.
Coach Vincenzo Montella, who coached Cuadrado at Fiorentina, said: “He’s a player for Chelsea, you are going to have to ask him.”
"Good players always have interest during the transfer window. He's a Chelsea player now.
"What happens in the future I can't answer for."
Inter Milan have also made a £30m inquiry for Chelsea’s Brazilian midfielder Oscar.
Conte said: "Zouma is improving a lot and this is good news. But we know that his injury was very bad and for this reason we must respect the time it takes.
"But for me it’s important to see he’s improving and I’m very happy for the guy because his injury was very bad."
